I mostly agree with @Jim French Stepstool
For the MLB portion of the rule 5 draft they have to be MLB players, so position players have to be much more advanced, and I just don't see Wood being advanced enough to occupy a spot, so he is safe.
Manfredi is tricky, like all relievers, they are the easiest to stash, but I just don't see him as consistent enough to warrant big league innings for most of the year. I hope he proves me wrong this year, but Jett and Adams could be big leaguers this year if there was a need, so a team would roll the dice on either one as an IF and pinch hitter and occasional starter.
Wagoner is tough until he hits AAA, but with that velocity he could deserve a spot, as velo guys are the ones teams will roll the dice on. Manfredi - with the number of LHP in the 'pen that the team could use (Hall, Ashby, Rob Z, Koenig plus Fitzpatrick if/when healthy, and Zerpa hopefully back sometime next year) Manfredi could be a trade candidate to give him a shot.